All categories

2 days ago

The number of students who chose lunch was 5 more than the number of students who chose breakfast. Write a system of linear equa

tions that represents the numbers of students who chose breakfast and lunch. Let x x represent the number of students who chose breakfast and y y represent the number of students who chose lunch. (50 students picked, 25 picked dinner the rest picked lunch and breakfast)

Mathematics

You might be interested in

Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes

Zina [12379]

Let x represent the number of caps

cost per cap = $6

cost for x caps = 6x

shipping charge = $25

overall budget = $1000

We can set up the following inequality:

Because the total amount cannot exceed 1000, we have

25 + 6x ≤ 1000

6x ≤ 975

x ≤ 162.5

rounding,

x ≤ 163

This means she can purchase a maximum of 163 caps.

5 0

3 months ago

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

PIT_PIT [12445]

Answer:

The tangent plane equation for the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

We have

The ellipsoid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation for the tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ (Given)

The hyperboloid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The tangent plane equation at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The tangent plane equation for the hyperboloid is

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The tangent plane equation

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required tangent plane equation for the hyperboloid is

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

7 0

3 months ago

According to Consumer Digest (July/August 1996), the probable location of personal computers (PC) in the home is as follows: Adu

PIT_PIT [12445]

Answer:

a) 0.32

b) 0.68

c) Office or den

Step-by-step explanation:

a) The likelihood that a personal computer is located in a bedroom can be calculated by adding the probabilities of it being in an adult bedroom, child bedroom, or another bedroom:

$P(B) =P(adult)+P(child)+P(other)\\P(B) = 0.03+0.15+0.14\\P(B) =0.32$

b) The probability of a PC not being located in a bedroom is found by calculating 100% minus the probability of it being in a bedroom:

$P(Not\ B) = 1- P(B)\\P(Not\ B) =1-0.32\\P(Not\ B) =0.68$

c) The expected location for finding a personal computer in a randomly selected household is derived from the room most likely to contain a PC according to Consumer Digest. The Office or den ranks as the most likely place with a probability of 0.40.

A PC would most likely be found in the Office or den.

6 0

2 months ago

A rectangle is transformed according to the rule r0, 90º. the image of the rectangle has vertices located at r'(–4, 4), s'(–4, 1

Svet_ta [12734]

Answer:

For a 90º clockwise rotation, the vertex q' (–3, 4) maps to q(4, 3).

According to the 90º counterclockwise rotation rule, q' (–3, 4) transforms to q(–4, –3).

Step-by-step explanation:

Given the rectangle with vertices r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4),

Find the image of vertex q after a 90º rotation.

The rotation rules are:

90º clockwise: (x, y) → (y, –x)

90º counterclockwise: (x, y) → (–y, x)

Applying the clockwise rule to q'(–3, 4) yields q(4, 3).

Applying the counterclockwise rule to q'(–3, 4) yields q(–4, –3).

Thus, clockwise rotation of q' (–3, 4) results in q(4, 3),

and counterclockwise rotation results in q(–4, –3).

4 0

3 months ago

Read 2 more answers